Expansible tube valves of the type shown in U.S. Pat. Nos. 3,272,470, 3,371,677, and 3,306,569 have enjoyed considerable commercial success, particularly in pressure regulation service. Such valves include a slotted core with a barrier across it between inlet and outlet flow slots. An expansible tube is stretched to seal around the barrier normally to isolate the inlet and outlet slots. The core and expansible tube are carried within a housing with a jacket fluid pressure normally asserted against the outer surface of the expansible tube. In such valves, the ends of the tube must be firmly anchored in place and must also seal around the core, and between the housing and the end closure. According to the existing configuration, the expansible tubes are provided with integrally molded flange members at the ends thereof, one extending inward and the other extending outward. Because the seal between body parts must be effected over a relatively broad area, i.e. over the flat surface of the flanges, it is necessary to provide an initial high clamping force between the parts so as to insure a fluid-tight seal. Accordingly, a high axial bolt loading is required in assembly of the valve. However, should the loading be excessive, it could produce high stresses in the rubber being squeezed, perhaps causing compression cracking and even failure of the flexible tube and the seal portions thereof. Short of such failure, excessive squeezing of the flanges could produce displacement of the rubber therein, changing the shape of the resilient tube in ways which are difficult to predict and, therefore, difficult to anticipate in design.